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By the method of contrapositive, check t...

By the method of contrapositive, check the validity of the statement: " If a, b in Z` such that ab is odd, then both 'a' and 'b' are odd".

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Write the converse and contrapositive of the statement " If x is a prime number then x is odd "

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Knowledge Check

  • The contrapositive of the statement " If vec a = vec 0 or vec b = vec 0 then vec a xx vec b = vec 0 " is

    A
    If `vec a xx vec b ne vec 0` then `vec a ne vec 0` or `vec b ne vec 0`
    B
    If `vec a xx vec b = 0` then `vec a = 0` or `vec b = vec 0`
    C
    If `vec a ne vec 0` and `vec a ne vec 0` then `vec a xx vec b ne vec 0`
    D
    If `vec a xx vec b` then `vec a ne vec 0` then `vec b ne vec 0`

  • Let A and B are matrices such that A+B and B A are both defined, then

    A
    1)A and B are square matrices of different order
    B
    2)A and B are square matrices of same order
    C
    3)A and B are of same order
    D
    4)number of columns of A= number of rows of B

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    Check the validity of the statements (i) 200 is multiple of 4 and 5 (ii) 240 is a multiple of 3 or 5

    Check whether the following statement is true or not. Id x, y in Z are such that x and y are odd, then xy is odd.

    Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.

    For each of the following compound statements, first identify the corresponding component statements. Then check whether the statements are true or not. If a and b are integers, then ab is a rational number.

    By giving counter example, show that the following statement is false. P : If n is an odd integer, then n is prime

    Given statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other. (b) If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. (ii) If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

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